SciPost Thesis Link
| Title: | Numerical study of the trapped and extended Bose-Hubbard models | |
| Author: | T. Comparin | |
| As Contributor: | Tommaso Comparin | |
| Type: | Master's | |
| Field: | Physics | |
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| Approaches: | Theoretical, Computational | |
| URL: | http://dspace.library.uu.nl/bitstream/handle/1874/280135/p_at_vw.pdf | |
| Degree granting institution: | Utrecht University | |
| Supervisor(s): | C. Morais Smith | |
| Defense date: | 2013-06-24 |
Abstract:
The Bose-Hubbard model describes the physics of a system of bosonic ultracold atoms in an optical lattice, in which a phase transition is present between a superfluid phase and a Mott insulator one. The exact solution of this Hamiltonian is only feasible to find the ground-state of small systems, while other techniques (as mean-field schemes or quantum Monte Carlo) are necessary to study systems of larger size. As a first application, we study the trapped model - relevant for the comparison with current experiments - through an inhomogeneous mean-field scheme. We describe some signatures of the phase crossover between superfluid and Mott insulator. In particular, the visibility of the quasimomentum distribution shows some kinks as a function of the lattice depth; we describe these features and we link them with the ones observed in other works in the literature. As a second application, we use quantum Monte Carlo techniques to study the one-dimensional Bose-Hubbard model with long-range interactions and we focus on the appearance of the Haldane insulating phase, distinguishable from the Mott one through the presence of non-local hidden order. Non-local correlation functions are also used to describe the difference between the superfluid phase and the Mott insulator one.